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It is well known that in special relativity observers can disagree on the time ordering of two events.

It is also well known that entangled particles exhibit so called spooky action at a distance.

Today I read in the New Scientist and on the arXiv that although the order of two events can be arbitrary, this is not so for multiple events. As the number of events increase the number of combinations of possible orders increase but not every one of these combinations will actually be possible to always observe.

According to the NS article it is possible to entangle three particles a,b and c and then have them in such a way that the collaspe of c cannot be observed to precede the collapse of both a and b by any observer even though c spookily causes the collapse of a and b.

Is this an outright contradiction between relativity and quantum mechanics or just a paradox ? What is the explantion ?

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There is nothing in QM that allows c to affect a and b instantaneously. An observer who can measure c and a will simply observe that they are correlated, but that can't happen until signals have arrived from both c and a. So no contradiction can be observed. C doesn't cause the collapse of a. Their entangled states just tells you what values of a can be observed. What is spooky is what happens to the other states of a, because inconsistent histories seem to just disappear when information from c is combined with the information from a.

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The correlations between the ways entangled particles are allowed to collapse are independent on the time ordering. For example, in the EPR experiment, if A and B are spacelike separated, one observer can see that the A wavefunction was collapsed first, and B second, and another observer can see the other ordering. There's no way to check which collapsed first, A or B. When we describe a quantum system, we use a preferred way to decompose spacetime in space + time. Some conclude from this that the collapse of A caused the collapse of B, and there's a causal connection between them (although they are spacelike separated). But this decomposition is not absolute, and should not be regarded as absolute. Any other decomposition will work, although the two collapses will appear in the reverse order. So we should not interpret causally the correlation between the collapse of A and that of B.

The paper shows that for three or more events some time orderings are forbidden, and we can construct the strange situation described in the question. This situation shows that we should not think that the collapses happen in a particular order in time. In other words, we can't find a decomposition of space + time which allows us to interpret that the one collapse caused the others. They just happen, and what matters is that they are correlated. The time ordering is just in the observer's eye.

So, my interpretation of these results is simply that thinking spacelike separated quantum events as happening in a particular time ordering has some limits. It doesn't contradict special relativity, it only contradicts the point that when two events are correlated, then one of them should be the cause of the other.

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Actually, this isn't much of a paradox at all. As long as c precedes a for some observer and c precedes b for some observer then c can cause a and b. c doesn't need to be seen to precede a and b by the same observer.

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